THE COMPOUND // FIELD NOTES // WEEK 12
Solving triangles and rationalizing
Field Book
Lessons 44 to 47
Due
Test 10 due ยท Supplement 12
Method
Paper first, every step
Escape 3 posts this week. Solving a triangle means all six measures: three sides, three angles, no partial credit from the Examiner.
What you have to be able to do
- Solve a right triangle for all six measures
- Apply the difference of squares theorem to equations
- Simplify radical expressions and convert rates
The procedures
Solve the triangleField Book Lesson 44
- List the six measures: three sides, three angles. Circle what is known.
- Use trig ratios for sides, inverse trig for angles, and the 180 sum to finish.
Difference of squares theoremField Book Lesson 45
- If A2 = B2, then A = B or A = -B.
- Every square root step in an equation carries the plus and the minus.
Radicals and fractional exponentsField Book Lesson 46
- Rationalize before building the LCD, same order as always.
- Convert between radical form and fractional exponent form freely.
Rate conversionsField Book Lesson 47
- Convert the top unit and the bottom unit separately.
- Stack the unit multipliers and cancel like factors.
Worked: both roots
- Solve A2 = 49.
- Take both square roots: A = 7 or A = -7.
Terms on the record
| Term | Meaning |
|---|
| solve the triangle | find all three sides and all three angles |
| radical expression | an expression containing a root sign |
| rate | a ratio of two measures with different units |